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I just remember a turbulence workshop where some people presented a Principal Orthogonal Decomposition of atmospheric data and waxed lyrical about it. "POD modes" are a great way to reduce the hell that is fluid dynamics to a finite-dimensional system of equations, but if you impose the POD modes you obtain for describing past history onto a model to try to predict future behaviour you cannot predict deviations from past history...

Of all the ways of organizing banking, the worst is the one we have today — Mervyn King, 25 October 2010
by Migeru (migeru at eurotrib dot com) on Fri Dec 10th, 2010 at 04:11:45 AM EST
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In layman's terms - if you try to predict the future based on (complex equations derived from) the past, all you can do is extrapolate the past, not predict new or deviations from past trends?  

But can you not factor in new data - e.g. increased CO2 levels - leading to significantly different results?

Index of Frank's Diaries

by Frank Schnittger (mail Frankschnittger at hot male dotty communists) on Fri Dec 10th, 2010 at 05:09:57 AM EST
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You can find different amplitudes, speeds, or signs of the oscillations, but if you write something like the NAO into your coordinates you may be unable to see the NAO being replaced by a substantively different pattern of variability.

The problem with dimension reduction (otherwise a very useful technique) is precisely that.

Of all the ways of organizing banking, the worst is the one we have today — Mervyn King, 25 October 2010

by Migeru (migeru at eurotrib dot com) on Fri Dec 10th, 2010 at 05:16:50 AM EST
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